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...he distance between node i and its user, dj,i is the distance between any other node j and the user of node i, N is the noise power. This definition maps to the well-known physical interference model =-=[7]-=-. The goal of spectrum allocation is to maximize a system utility function based on the achieved throughput for each node-user pair i. Define the achieved throughput for each node-user pair i as Ai = ...

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...k, regardless of their location. B. Conflict-Graph Based Simplification Prior work in this area simplifies the problem using a conflict-graph based interference model, or the so-called protocol model =-=[8]-=-. This model reduces the accumulative interference conditions into a set of pairwise interference constraints. Any two transmissions either conflict and cannot use the same channels concurrently or th...

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...orm interference conditions. In practice, nodes experience heterogeneous interference conditions because of the nonuniform node density, AP-user distance and transmit power. For example, measurements =-=[10]-=- show that APs are highly clustered, and their interference conditions vary significantly over locations. To address such heterogeneity, PLAN introduces a local conflict adjustment algorithm to adjust...

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...one of them is on. In [13], two links are declared conflicting if the total throughput when both links are active is significantly lower than the total throughput when only one is active. The work in =-=[15]-=- improves the measurement scalability by developing theoretical models on RSSI measurements. Finally, a proactive probing approach was proposed by [1] to determine the quality of transmissions when bo...

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...nt spectrum allocation solutions. On the other hand, recent works have shown that the use of conflict graph based interference models, could lead to large performance degradation in wireless networks =-=[4]-=-, [12]. In its current design, the model fails to capture the cumulative effect of interference. Simultaneous activation of multiple links can cause enough cumulated interference to disrupt a transmis...

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... Therefore, PLAN can make the allocation adjustments using a commodity radio hardware. B. Integrating Power Control Power control has been proposed to control network topology, increase spacial reuse =-=[2]-=- and reduce interference. Intuitively, PLAN can be integrated with power control. For downlink transmissions (AP to user), APs can first transmit at the highest power and then apply PLAN and a channel...

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...solutions to define conflict graphs. To determine whether two links conflict, they perform isolated measurements on the transmission quality when both links are on and when only one of them is on. In =-=[13]-=-, two links are declared conflicting if the total throughput when both links are active is significantly lower than the total throughput when only one is active. The work in [15] improves the measurem...

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... Because the multi-tier interference metric over-estimates the interference, this maps to the upper bound rub on r. 2) Single-tier Interference: When estimating the interference, previous literatures =-=[9]-=-, [20] consider only the first tier of nodes because they produce the majority of the interference. In this case, the total interference only counts those of the 6 closest neighbors in Fig. 4: I(r) = ...

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...use the multi-tier interference metric over-estimates the interference, this maps to the upper bound rub on r. 2) Single-tier Interference: When estimating the interference, previous literatures [9], =-=[20]-=- consider only the first tier of nodes because they produce the majority of the interference. In this case, the total interference only counts those of the 6 closest neighbors in Fig. 4: I(r) = 6 · P ...

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...ity is required to optimize the spectrum allocation. Prior work on spectrum management simplifies this problem by assuming radio interference can be modeled by a conflict graph [5], [11], [14], [19], =-=[21]-=-, [22]. The effect of interference is abstracted into pairwise binary metrics between transmissions. Two transmissions either conflict when using the same spectrum channel, or can use the same channel...

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...st show two theorems on µ. Theorem 2: Given a conflict graph, we can achieve µ ≥ using a simple greedy spectrum allocation algorithm. 1 ∆+1 Proof: The theorem follows directly from a theorem of Turán =-=[18]-=-, which analyzes a simple greedy allocation algorithm as follows. “Starting from the allocation when all nodes are inactive, iteratively pick the node with smallest degree (if there are multiple nodes...

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...al interference model and the graph model is an interesting problem. Recent literatures have found fundamental differences between the two in terms of wireless capacity and link scheduling efficiency =-=[6]-=-, [12]. In this paper, we found somewhat surprisingly that the graph model can achieve the same optimal result as the physical model in terms of spectrum allocation. Our results validate the use of gr...

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...ectrum allocation solutions. On the other hand, recent works have shown that the use of conflict graph based interference models, could lead to large performance degradation in wireless networks [4], =-=[12]-=-. In its current design, the model fails to capture the cumulative effect of interference. Simultaneous activation of multiple links can cause enough cumulated interference to disrupt a transmission e...

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...ignificant complexity is required to optimize the spectrum allocation. Prior work on spectrum management simplifies this problem by assuming radio interference can be modeled by a conflict graph [5], =-=[11]-=-, [14], [19], [21], [22]. The effect of interference is abstracted into pairwise binary metrics between transmissions. Two transmissions either conflict when using the same spectrum channel, or can us...

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... throughput when only one is active. The work in [15] improves the measurement scalability by developing theoretical models on RSSI measurements. Finally, a proactive probing approach was proposed by =-=[1]-=- to determine the quality of transmissions when both links transmit. Under the physical interference model defined by (1), the equivalent approach to the above solutions is to perform the isolated pai...

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... optimization techniques such as graph-coloring and local search can be applied to produce efficient solutions to (4). Prior works have developed both centralized and distributed solutions [5], [14], =-=[16]-=-, [22]. C. Deriving Conflict Graphs While extensive efforts have been devoted to developing efficient allocation algorithms under the graph interference model, little consideration is given to derivin...

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... required to optimize the spectrum allocation. Prior work on spectrum management simplifies this problem by assuming radio interference can be modeled by a conflict graph [5], [11], [14], [19], [21], =-=[22]-=-. The effect of interference is abstracted into pairwise binary metrics between transmissions. Two transmissions either conflict when using the same spectrum channel, or can use the same channel concu...

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...hus significant complexity is required to optimize the spectrum allocation. Prior work on spectrum management simplifies this problem by assuming radio interference can be modeled by a conflict graph =-=[5]-=-, [11], [14], [19], [21], [22]. The effect of interference is abstracted into pairwise binary metrics between transmissions. Two transmissions either conflict when using the same spectrum channel, or ...

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...omplexity is required to optimize the spectrum allocation. Prior work on spectrum management simplifies this problem by assuming radio interference can be modeled by a conflict graph [5], [11], [14], =-=[19]-=-, [21], [22]. The effect of interference is abstracted into pairwise binary metrics between transmissions. Two transmissions either conflict when using the same spectrum channel, or can use the same c...

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...cant complexity is required to optimize the spectrum allocation. Prior work on spectrum management simplifies this problem by assuming radio interference can be modeled by a conflict graph [5], [11], =-=[14]-=-, [19], [21], [22]. The effect of interference is abstracted into pairwise binary metrics between transmissions. Two transmissions either conflict when using the same spectrum channel, or can use the ...

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...riation of graph coloring model. [5], [22] proposed low-complexity algorithms based on local adaptation. [16] proposed algorithms that optimize channel allocation by considering APs’ traffic demands. =-=[3]-=- designed centralized algorithms to assign spectrum blocks that are contiguous in frequency. Our allocation-aware analytical framework in this paper can be used in conjunction with the above algorithm...

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.... We then use this measure to determine the r required to guarantee that all the active transmissions are successful. 1) Multi-tier Interference: In the worst interference case, we know from geometry =-=[17]-=- that the nodes allocated with the same channel form a hexagonal topology shown in Fig. 4. When considering the interference produced by all the nodes, the center node’s transmission will experience t...